A system of equations in the unknowns a b c d e is represent

A system of equations in the unknowns a, b, c, d, e is represented by an augmented matrix whose reduced row-echelon form is as shown. Find all the solutions in terms of parameters s and t. (1 0 0 0 1 0 6 4 0 0 0 1 5 3 2 | 7 8 9)

Solution

Your matrix

Find the pivot in the 1st column in the 1st row

Find the pivot in the 2nd column in the 2nd row

Find the pivot in the 4th column in the 3rd row

solution

a = 7 - 6t - 5s

b = 8 - 4t - 3s

d = 9 - 2s

c = t , e = s

	X1	X2	X3	X4	X5	b
1	1	0	6	0	5	7
2	0	1	4	0	3	8
3	0	0	0	1	2	9